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Fractional Quadrature rule and using its Exactness for the Müntz-Legendre Scaling Functions for Solving Fractional Differential Equations
Ritu Kumari, Mani Mehra, Abhishek Kumar Singh
Fractional operators (derivatives/integrals) are defined via the integration of the functions. When the function is produced by a spanning set of fractional power functions, tradit…
Modified least squares method and a review of its applications in machine learning and fractional differential/integral equations
Abhishek Kumar Singh, Mani Mehra, Anatoly A. Alikhanov
The least squares method provides the best-fit curve by minimizing the total squares error. In this work, we provide the modified least squares method based on the fractional ortho…
High order approximation to Caputo derivative on graded mesh and time-fractional diffusion equation for non-smooth solutions
Shweta Kumari, Abhishek Kumar Singh, Vaibhav Mehandiratta +1
In this paper, a high-order approximation to Caputo-type time-fractional diffusion equations involving an initial-time singularity of the solution is proposed. At first, we employ…
The Crank-Nicholson type compact difference scheme for a loaded time-fractional Hallaire's equation
Anatoly Alikhanov, Murat Beshtokov, Mani Mehra
In this paper, we study loaded modified diffusion equation (the Hallaire equation with the fractional derivative with respect to time). The compact finite difference scheme of Cran…